Hii

Admission to AIIMS institutes are nowhere dependent on NEET. NEET provides admission to all the colleges under MCI while the AIIMS institute is a government college governed by the ANI. For getting admission to AIIMS, you need to qualify AIIMS MBBS Entrance which is scheduled to be held on 25th and 26th of May this year.
You need to prepare extreamly well as the competition as well as the cutoff is very high in AIIMS.
In NEET, the level of questions is a bit less than those asked in AIIMS. Also, AIIMS has a section of GK and Current Affairs while NEET does not have questions from GK.
For AIIMS MBBS Exam, you need to have a strong hold on your basics i.e NCERT but along with NCERT you need a bit higher knowledge so you must refer to some reference books like 
Physics- 

• DC pandey objective Physics
• Universal selfscorer
• Concepts of physics by HC Verma Vol 1 & 2
• AIIMS Explorer fromMTG editorials

Chemistry - 

• Physical chemistry by OP Tondon
• Textbook of organic chemistry from arihant publications
• Modern's ABC of chemistry vol 1 & 2
• Objective chemistry by S.Dinesh

Biology -

• Trueman's Biology vol 1 & 2
• Objective biology by S.Dinesh
• Exploring biology from arihant publications.

General Knowledge -

• Aim4Aiims by Ajay mohan
  
• GK Books by ajay mohan
  
• General knowledge, apitude and logical reasoning for AIIMS by Sunil Nain

Study hard and try your best, do not get demotivated if you haven't qualified NEET, try your best for AIIMS and hope for the best.
Give it your best shot and stay confident.

Hope this helps
All The Best!!

Both the exams are independent and disqualification in one does not effect the other. NEET provides admission to colleges under MCI whereas AIIMS are autonomous institutions governed by Act of National Importance.

However,it must be noted that eligibility criteria of both NEET and AIIMS are almost same ( AIIMS needs 60% overall whereas NEET requires 50%). 

Hence, it can be assumed if one is ineligible for NEET he may be so for AIIMS.